arXiv subjects

Richard Berk

Publications and source records attributed to Richard Berk.

14 recordsLinked to original sources

arXiv2025

Forecasting Arctic Temperatures With Quantile Machine Learning

Using data from the Longyearbyen weather station, quantile gradient boosting ("small AI") is applied to forecast daily temperatures in Svalbard, Norway. Temperatures above 0 degrees Celsius are of special interest because of their impact on ice, snow, and tundra permafrost. To improve forecasting skill for warmer temperatures, the target quantile is 0.60; forecast underestimates are weighted 1.5 times more heavily than forecast overestimates when the quantile loss is computed. Predictors include eight routinely collected indicators of weather conditions, each lagged by 14 days, yielding temperature forecasts with a two-week lead time. Adaptive conformal prediction regions quantify forecasting uncertainty with provably valid coverage. Using a holdout sample, a forecast of 0 degrees Celsius is correct 14 days later at least 80% of the time. Implications for Arctic adaptation policy are discussed.

stat.AP↗

arXiv2025

Forecasting Extreme Day and Night Heat in Paris: A Proof of Concept

As a form of "small A", quantile machine learning is used to forecast diurnal and nocturnal $Q(.90)$ air temperatures for Paris, France from late spring through the summer months of 2021. The data are provided by the Paris-Montsouris weather station. Rather than trying to directly anticipate the onset and cessation of reported heat waves, Q(.90) values are estimated. The 90th percentile is chosen so that exceedances represent relatively rare and extreme conditions. Predictors include eight routinely available indicators of weather conditions, lagged by 14 days. Using holdout data, the temperature forecasts are produced two weeks in advance. Adaptive conformal prediction regions are computed that, under exchangeability, provide provably valid finite-sample coverage of forecasting uncertainty. For both diurnal and nocturnal temperatures, forecasting accuracy in the holdout data is promising, and sound measures of uncertainty are coupled with a novel decision-making framework. Benefits for policy and practice follow.

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arXiv2025

Demystifying AI in Criminal Justice

There is widespread confusion among criminal justice practitioners and legal scholars about the use of artificial intelligence in criminal justice. This didactic review is written for readers with little or no background in statistics or computer science. It is not intended to replace more technical treatments. It is intended to supplement them and encourage readers to dig more deeply into topics that strike their fancy.

cs.CY↗

arXiv2021

Semi-Supervised linear regression

We study a regression problem where for some part of the data we observe both the label variable ($Y$) and the predictors (${\bf X}$), while for other part of the data only the predictors are given. Such a problem arises, for example, when observations of the label variable are costly and may require a skilled human agent. When the conditional expectation $E[Y | {\bf X}]$ is not exactly linear, one can consider the best linear approximation to the conditional expectation, which can be estimated consistently by the least squares estimates (LSE). The latter depends only on the labeled data. We suggest improved alternative estimates to the LSE that use also the unlabeled data. Our estimation method can be easily implemented and has simply described asymptotic properties.The new estimates asymptotically dominate the usual standard procedures under certain non-linearity condition of $E[Y | {\bf X}]$; otherwise, they are asymptotically equivalent.The performance of the new estimator for small sample size is investigated in an extensive simulation study. A real data example of inferring homeless population is used to illustrate the new methodology.

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arXiv2020

Evaluating the Effectiveness of Personalized Medicine with Software

We present methodological advances in understanding the effectiveness of personalized medicine models and supply easy-to-use open-source software. Personalized medicine involves the systematic use of individual patient characteristics to determine which treatment option is most likely to result in a better outcome for the patient on average. Why is personalized medicine not done more in practice? One of many reasons is because practitioners do not have any easy way to holistically evaluate whether their personalization procedure does better than the standard of care. Our software, "Personalized Treatment Evaluator" (the R package PTE), provides inference for improvement out-of-sample in many clinical scenarios. We also extend current methodology by allowing evaluation of improvement in the case where the endpoint is binary or survival. In the software, the practitioner inputs (1) data from a single-stage randomized trial with one continuous, incidence or survival endpoint and (2) a functional form of a model for the endpoint constructed from domain knowledge. The bootstrap is then employed on data unseen during model fitting to provide confidence intervals for the improvement for the average future patient (assuming future patients are similar to the patients in the trial). One may also test against a null scenario where the hypothesized personalization are not more useful than a standard of care. We demonstrate our method's promise on simulated data as well as on data from a randomized comparative trial investigating two treatments for depression.

stat.ME↗

arXiv2019

Models as Approximations I: Consequences Illustrated with Linear Regression

In the early 1980s Halbert White inaugurated a "model-robust'' form of statistical inference based on the "sandwich estimator'' of standard error. This estimator is known to be "heteroskedasticity-consistent", but it is less well-known to be "nonlinearity-consistent'' as well. Nonlinearity, however, raises fundamental issues because in its presence regressors are not ancillary, hence can't be treated as fixed. The consequences are deep: (1)~population slopes need to be re-interpreted as statistical functionals obtained from OLS fits to largely arbitrary joint $\xy$~distributions; (2)~the meaning of slope parameters needs to be rethought; (3)~the regressor distribution affects the slope parameters; (4)~randomness of the regressors becomes a source of sampling variability in slope estimates; (5)~inference needs to be based on model-robust standard errors, including sandwich estimators or the $\xy$~bootstrap. In theory, model-robust and model-trusting standard errors can deviate by arbitrary magnitudes either way. In practice, significant deviations between them can be detected with a diagnostic test.

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arXiv2019

Models as Approximations II: A Model-Free Theory of Parametric Regression

We develop a model-free theory of general types of parametric regression for iid observations. The theory replaces the parameters of parametric models with statistical functionals, to be called "regression functionals'', defined on large non-parametric classes of joint $\xy$ distributions, without assuming a correct model. Parametric models are reduced to heuristics to suggest plausible objective functions. An example of a regression functional is the vector of slopes of linear equations fitted by OLS to largely arbitrary $\xy$ distributions, without assuming a linear model (see Part~I). More generally, regression functionals can be defined by minimizing objective functions or solving estimating equations at joint $\xy$ distributions. In this framework it is possible to achieve the following: (1)~define a notion of well-specification for regression functionals that replaces the notion of correct specification of models, (2)~propose a well-specification diagnostic for regression functionals based on reweighting distributions and data, (3)~decompose sampling variability of regression functionals into two sources, one due to the conditional response distribution and another due to the regressor distribution interacting with misspecification, both of order $N^{-1/2}$, (4)~exhibit plug-in/sandwich estimators of standard error as limit cases of $\xy$ bootstrap estimators, and (5)~provide theoretical heuristics to indicate that $\xy$ bootstrap standard errors may generally be more stable than sandwich estimators.

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arXiv2017

A Convex Framework for Fair Regression

We introduce a flexible family of fairness regularizers for (linear and logistic) regression problems. These regularizers all enjoy convexity, permitting fast optimization, and they span the rang from notions of group fairness to strong individual fairness. By varying the weight on the fairness regularizer, we can compute the efficient frontier of the accuracy-fairness trade-off on any given dataset, and we measure the severity of this trade-off via a numerical quantity we call the Price of Fairness (PoF). The centerpiece of our results is an extensive comparative study of the PoF across six different datasets in which fairness is a primary consideration.

cs.LG↗

arXiv2017

Calibrated Percentile Double Bootstrap For Robust Linear Regression Inference

We consider inference for the parameters of a linear model when the covariates are random and the relationship between response and covariates is possibly non-linear. Conventional inference methods such as z-intervals perform poorly in these cases. We propose a double bootstrap-based calibrated percentile method, perc-cal, as a general-purpose CI method which performs very well relative to alternative methods in challenging situations such as these. The superior performance of perc-cal is demonstrated by a thorough, full-factorial design synthetic data study as well as a real data example involving the length of criminal sentences. We also provide theoretical justification for the perc-cal method under mild conditions. The method is implemented in the R package `perccal', available through CRAN and coded primarily in C++, to make it easier for practitioners to use.

stat.ME↗

arXiv2014

Using Regression Kernels to Forecast A Failure to Appear in Court

Forecasts of prospective criminal behavior have long been an important feature of many criminal justice decisions. There is now substantial evidence that machine learning procedures will classify and forecast at least as well, and typically better, than logistic regression, which has to date dominated conventional practice. However, machine learning procedures are adaptive. They "learn" inductively from training data. As a result, they typically perform best with very large datasets. There is a need, therefore, for forecasting procedures with the promise of machine learning that will perform well with small to moderately-sized datasets. Kernel methods provide precisely that promise. In this paper, we offer an overview of kernel methods in regression settings and compare such a method, regularized with principle components, to stepwise logistic regression. We apply both to a timely and important criminal justice concern: a failure to appear (FTA) at court proceedings following an arraignment. A forecast of an FTA can be an important factor is a judge's decision to release a defendant while awaiting trial and can influence the conditions imposed on that release. Forecasting accuracy matters, and our kernel approach forecasts far more accurately than stepwise logistic regression. The methods developed here are implemented in the R package kernReg currently available on CRAN.

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arXiv2013

Improved Precision in Estimating Average Treatment Effects

The Average Treatment Effect (ATE) is a global measure of the effectiveness of an experimental treatment intervention. Classical methods of its estimation either ignore relevant covariates or do not fully exploit them. Moreover, past work has considered covariates as fixed. We present a method for improving the precision of the ATE estimate: the treatment and control responses are estimated via a regression, and information is pooled between the groups to produce an asymptotically unbiased estimate; we subsequently justify the random X paradigm underlying the result. Standard errors are derived, and the estimator's performance is compared to the traditional estimator. Conditions under which the regression-based estimator is preferable are detailed, and a demonstration on real data is presented.

stat.ME↗

arXiv2013

Valid post-selection inference

It is common practice in statistical data analysis to perform data-driven variable selection and derive statistical inference from the resulting model. Such inference enjoys none of the guarantees that classical statistical theory provides for tests and confidence intervals when the model has been chosen a priori. We propose to produce valid ``post-selection inference'' by reducing the problem to one of simultaneous inference and hence suitably widening conventional confidence and retention intervals. Simultaneity is required for all linear functions that arise as coefficient estimates in all submodels. By purchasing ``simultaneity insurance'' for all possible submodels, the resulting post-selection inference is rendered universally valid under all possible model selection procedures. This inference is therefore generally conservative for particular selection procedures, but it is always less conservative than full Scheffe protection. Importantly it does not depend on the truth of the selected submodel, and hence it produces valid inference even in wrong models. We describe the structure of the simultaneous inference problem and give some asymptotic results.

math.ST↗

arXiv2010

Small area estimation of the homeless in Los Angeles: An application of cost-sensitive stochastic gradient boosting

In many metropolitan areas efforts are made to count the homeless to ensure proper provision of social services. Some areas are very large, which makes spatial sampling a viable alternative to an enumeration of the entire terrain. Counts are observed in sampled regions but must be imputed in unvisited areas. Along with the imputation process, the costs of underestimating and overestimating may be different. For example, if precise estimation in areas with large homeless c ounts is critical, then underestimation should be penalized more than overestimation in the loss function. We analyze data from the 2004--2005 Los Angeles County homeless study using an augmentation of $L_1$ stochastic gradient boosting that can weight overestimates and underestimates asymmetrically. We discuss our choice to utilize stochastic gradient boosting over other function estimation procedures. In-sample fitted and out-of-sample imputed values, as well as relationships between the response and predictors, are analyzed for various cost functions. Practical usage and policy implications of these results are discussed briefly.

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arXiv2008

Counting the homeless in Los Angeles County

Over the past two decades, a variety of methods have been used to count the homeless in large metropolitan areas. In this paper, we report on an effort to count the homeless in Los Angeles County, one that employed the sampling of census tracts. A number of complications are discussed, includingÊ the need to impute homeless counts to areas of Êthe CountyÊ not sampled. We conclude that, despite their imperfections, estimated counts provided useful and credible information to the stakeholders involved.

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